Close-in orbits in the restricted problem of three bodies
Author:
Richard B. Barrar
Journal:
Quart. Appl. Math. 27 (1969), 396-398
MSC:
Primary 85.34
DOI:
https://doi.org/10.1090/qam/255225
MathSciNet review:
255225
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Abstract: Utilizing a transformation due to Birkhoff [3], we establish for the restricted problem of three bodies the existence of conditionally periodic orbits that move in a small neighborhood of one of the primaries. These orbits result from perturbation of elliptic orbits and are valid for all mass ratios of the two primaries.
- Richard F. Arenstorf, A new method of perturbation theory and its application to the satellite problem of celestial mechanics, J. Reine Angew. Math. 221 (1966), 113–145. MR 189785, DOI https://doi.org/10.1515/crll.1966.221.113
- Richard Barrar, A proof of the convergence of the Poincaré-von Zeipel procedure in celestial mechanics, Amer. J. Math. 88 (1966), 206–220. MR 199490, DOI https://doi.org/10.2307/2373056
G. Birkhoff, The restricted problem of three bodies, Rend. Circ. Mat. Palermo 39, 265–334 (1915)
- Charles Conley, On some new long periodic solutins of the plane restricted three body problem, Comm. Pure Appl. Math. 16 (1963), 449–467. MR 154724, DOI https://doi.org/10.1002/cpa.3160160405
H. Poincaré, Les méthodes nouvelles de la mécanique celeste, v. I (1892); Reprint, Dover, New York, 1957.
- Carl Ludwig Siegel, Vorlesungen über Himmelsmechanik, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956 (German). MR 0080009
A. Wintner, Über eine Revision der Sortentheorie des restringierten Dreikörperproblems, Sitzungsberichte der Sächsischen Akademie der Wissenschaften zu Leipzig, 82, 3–56 (1930)
R. F. Arenstorf, A new method of perturbation theory and its application to the satellite problem of celestial mechanics, J. Reine Angew. Math. 221, 113–145 (1966)
R. B. Barrar, A proof of the convergence of the Poincaré-von Zeipel procedure in celestial mechanics, Amer. J. Math. 88, 206–220 (1966)
G. Birkhoff, The restricted problem of three bodies, Rend. Circ. Mat. Palermo 39, 265–334 (1915)
C. C. Conley, On some new long periodic solutions of the plane restricted three body problem, Comm. Pure Appl. Math. 16, 449–467 (1963)
H. Poincaré, Les méthodes nouvelles de la mécanique celeste, v. I (1892); Reprint, Dover, New York, 1957.
C. L. Siegel, Vorlesungen über Himmelsmechanik, Springer-Verlag, Berlin, 1956, §23.
A. Wintner, Über eine Revision der Sortentheorie des restringierten Dreikörperproblems, Sitzungsberichte der Sächsischen Akademie der Wissenschaften zu Leipzig, 82, 3–56 (1930)
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Article copyright:
© Copyright 1969
American Mathematical Society
